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Robert F. Handschuh and Andrew J. ZakrajsekGlenn Research Center, Cleveland, Ohio
High-Pressure Angle Gears: Comparison to Typical Gear Designs
NASA/TM—2010-216251/REV1
June 2012
This printing replaces NASA/TM—2010-216251, March 2010.
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Robert F. Handschuh and Andrew J. ZakrajsekGlenn Research Center, Cleveland, Ohio
High-Pressure Angle Gears: Comparison to Typical Gear Designs
NASA/TM—2010-216251/REV1
June 2012
National Aeronautics andSpace Administration
Glenn Research CenterCleveland, Ohio 44135
Available from
NASA Center for Aerospace Information7115 Standard DriveHanover, MD 21076–1320
National Technical Information Service5301 Shawnee Road
Alexandria, VA 22312
Available electronically at http://www.sti.nasa.gov
Level of Review: This material has been technically reviewed by technical management.
Document Change History
NASA/TM—2010-216251/REV1, June 2012
High-Pressure Angle Gears: Comparison to Typical Gear DesignsRobert F. Handschuh and Andrew J. Zakrajsek
This printing replaces NASA/TM—2010-216251, March 2010; extensive changes were made to the document.
High-Pressure Angle Gears: Comparison to Typical Gear Designs
Robert F. Handschuh and Andrew J. Zakrajsek National Aeronautics and Space Administration
Glenn Research Center Cleveland, Ohio 44135
Abstract
A preliminary study has been completed to determine the feasibility of using high-pressure angle gears in aeronautic and space applications. Tests were conducted in the NASA GRC Spur Gear Test Facility at speeds up to 10,000 rpm and 73 N*m (648 in.-lb) for 3.18, 2.12, and 1.59 module gears (8, 12, and 16 diametral pitch gears), all designed to operate in the same test facility. The 3.18 module (8-diametral pitch), 28 tooth, 20 degree pressure angle gears are the NASA GRC baseline test specimen. Also, 2.12 module (12-diametral pitch), 42 tooth, 25 degree pressure angle gears were tested. Finally, 1.59 module (16-diametral pitch), 56 tooth, 35 degree pressure angle gears were tested. The high-pressure angle gears were the most efficient when operated in the high-speed aerospace mode (10,000 rpm, lubricated with a synthetic turbine engine oil) and produced the lowest wear rates when tested with a perfluoroether-based grease. The grease tests were conducted at 150 rpm and 71 N*m (630 in.-lb).
Introduction
Gearing is chosen very carefully for any given application to have a sufficient strength (load capacity) and, therefore, a long life before one of the many failure mechanisms initiates and results in component failure. Operating in very hostile environment conditions, such as large temperature swings, very abrasive dust, the use of nontraditional terrestrial lubricants, etc., premature failure can result (Refs. 1 and 2). In an attempt to improve gear performance, high-pressure angle (HPA) gearing is examined for possible use in space mechanism applications. As the pressure angle of a gear mesh increases, the rate of sliding of the surfaces over each other is reduced (Refs. 3 to 6). There are limits to how much the pressure angle can be increased as the design can eventually have a contact ratio approaching one and/or the tooth top land can become pointed. An approach to circumvent this dilemma is to make the gear mesh helical and use the face contact ratio to boost the overall contact ratio to a value greater than one (Refs. 7 and 8).
Gear Design and Analysis
To understand the effects of pressure angle increase, an analysis used for gear tooth contact fatigue was utilized. A computer code developed at NASA (Ref. 9) was used to calculate various parameters, including the sliding velocity of the teeth, and the resultant gear meshing power losses. The difference in sliding velocity between two of the designs tested is shown in Figure 1. The sliding velocity as a function of meshing position is shown for the 88.9 mm (3.5 in.) center distance (1:1 ratio) and two gear types—the standard 3.18 module (8 diametral pitch) 20 degree pressure angle and the high-pressure angle gears with 1.59 module (16 diametral pitch) and a 35 degree pressure angle.
There are other design considerations when changing to a higher-pressure angle. When trying to modify a design the pressure angle can only be modified so far for any given diametral pitch before tooth pointing can be design limiting. In the design mentioned in this report, the 35 degree pressure angle required doubling the diametral pitch. This increased the tooth count from 28 to 56 teeth. Also, due to the tooth pointing issues and the size of the teeth, the gear material, and the heat treatment process employed required modification. Instead of using 9310 gear steel and carburizing, Nitralloy 135M material using a nitriding heat treatment was chosen (very thin, hardened surface layer). With this material and heat-treat
NASA/TM—2010-216251/REV1 1
Figure 1.—Effect of gear design on sliding velocity at any point along the line of action
between 3.18 and 1.59 module (8 and 16 diametral pitch) gears for a 1:1 ratio.
TABLE 1.—RESULTS FROM PERFORMANCE (EFFICIENCY) AND LOAD CAPACITY ANALYSIS CODES Standard gear
geometry #1 Standard gear geometry #2
High pressure angle
Number of teeth 28 42 56 Gear material AISI 9310 AISI 9310 Nitralloy 135M Module, mm (diametral pitch, 1/in.) 3.18 (8) 2.12 (12) 1.59 (16) Pressure angle, degrees 20 25 35 Addendum, mm (in.) 3.18 (0.125) 2.12 (0.083) 1.40 (.055) Outside diameter, mm (in.) 95.25 (3.75) 93.17 (3.668) 91.69 (3.610) Chordal tooth thickness, mm (in.) 4.85 (0.191) 3.25 (0.128) 2.41 (0.095) Clearance, mm (in.) 0.79 (0.031) 0.79 (0.031) 0.19 (0.0075) Face width, mm (in.) 6.35 (0.25) 6.35 (0.25) 6.35 (0.25) Center distance, mm (in.) 88.9 (3.5) 88.9 (3.5) 88.9 (3.5) Profile shift (-) 0 0 0 Backlash, mm (in.) 0.15 (0.006) 0.15 (0.006) 0.076 (0.003) Contact ratio 1.64 1.53 1.16 Efficiency, load, and stress, at 10000 rpm,
71 N*m (630 in*lb) torque
Efficiency, % 99.41 99.62 99.77 Tangential load, N (lbs) 1601.4 (360) 1601.4 (360) 1601.4 (360) Radial load, N (lbs) 582.7 (131.0) 746.9 (167.9) 1121.4 (252.1) Bending stress, GPa, (ksi) 0.246 (35.7) 0.353 (51.2) 0.308 (44.6) Contact stress, GPa (ksi) 1.09 (158.1) 1.03 (149.3) 0.89 (129.1)
Note: Bending and contact stress found via ISO6336 (Ref. 10). change the gears could be normally manufactured without the threat of tooth capping. Capping occurs when carburized surfaces come together at thin material regions, such as at the top of the tooth, and the induced stress field, from the heat-treating process, causes the material to fracture even without an applied load.
The designs and the results of analysis are shown in Table 1. Calculations were made for the gears operating at 10,000 rpm using a synthetic aerospace lubricant. The one item to note in the table is that while the tangential load is the same (torque), the separating force between the gears has nearly doubled with the high-pressure angle design. While the design changes reduced the gearing losses, they increased the load the bearings must carry.
NASA/TM—2010-216251/REV1 2
ISO 6336 analysis was conducted on these three gear designs for tooth bending and contact stress. The results are shown in Table 1. From Table 1, the results between the three designs were fairly comparable with the 3.18 module (8 diametral pitch) gears having the lowest bending stress and the 1.59 module (16 diametral pitch) gears having the lowest contact stress.
Experimental Results Test procedure: Testing was done in two different modes for the gears evaluated in this study. The
basic properties of the two lubricants used are provided in Table 2. In the high-speed test mode, the gears were lubricated with a synthetic turbine engine lubricant. The gear mesh was lubricated with the jet pointing into mesh. The lubricant is gravity drained and returned to the lubricant reservoir. Lubricant temperature was measured just prior to the jet and at the exit region (drain) of the test gear cover. The load applied was measured statically using a torque wrench and was proportional to the torque actuator pressure applied. For these high-speed tests, the facility was brought up to full speed (10,000 rpm) prior to increasing the load to the maximum conditions tested.
In the low-speed, grease-lubricated mode, both the gears and the amount of grease applied were weighed prior to testing, and the gears were also weighed post test. Gears were rotated up to the 150 rpm condition where tests were run prior to increasing to the maximum load applied (pressure on torque actuator).
High-Speed Aerospace (Rotorcraft) Operation Three-gear designs were tested in the same gearbox, at identical rotational speed, torque, lubricant,
and inlet temperature. A photograph of the three designs tested is shown in Figure 2. The test rig used in this study is shown schematically in Figure 3. In this test rig, the drive motor only needs to provide enough power to overcome the losses within the geared system. A rotating torque actuator uses fluid pressure to apply torque by rotating one of the slave gears (shown in green) relative to its shaft. The test gears are shown in red in the figure. Tests were conducted at full-face width contact for all tests.
TABLE 2.—BASIC PROPERTIES OF THE TWO LUBRICANTS USED IN THIS STUDY Turbine engine lubricant Space grease Mixture Synthetic ester blend Base oil-perfluorinated polyether Pour point, °C (°F) –62 (–80) –73 (–100) Specific gravity 1 1.85 Viscosity, cSt. at 38 °C, 100 °F 29.2 148 Viscosity, cSt. at 100 °C, 210 °F 5.3 45
Figure 2.—Left to right: 3.18, 2.12, and 1.59 module (8, 12, and 16 diametral pitch) test gears.
NASA/TM—2010-216251/REV1 3
Figure 3.—Test facility at NASA Glenn Research Center.
Figure 4.—Temperature results for three different gearing configurations. All tests
conducted at 10,000 rpm, 71 N*m (630 in.-lb). Flow rate at 40 psi 8.1 ml/s (0.13 gpm).
The gears were tested at three levels of lubricant jet pressure (flow). The lubricant inlet and outlet temperatures were monitored throughout the tests. The data acquired for each gear design is shown in Figure 4. Seven different tests were conducted to generate the data shown in Figure 4. A comparison of the results indicates there is a definite difference between the three gear designs.
The lubricant temperature rise across a gearbox is a function of the gear meshing losses and any resultant windage losses. Pitch line velocity for these tests was 48.8 m/s (9160 ft/min). Finer pitch teeth with high-pressure angle showed an improvement resulting in a lower temperature change across the gearbox. Lubricant jet pressure (flow) into the gearbox had a lesser effect for each of the gear configurations, but there was a definite trend of lower temperature difference as the jet pressure was increased. It would be expected that heat removed from the gearbox should be related to TCm p∆ (lubricant flow rate, heat capacity of the lubricant, and the temperature difference between inlet and outlet for the lubricant) if other effects are neglected.
NASA/TM—2010-216251/REV1 4
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NASA/TM—2010-216251/REV1 7
Figure 11.—Shrouds on the high-pressure angle gears during tests.
Conclusions Based on the results obtained in this study, the following conclusions can be drawn:
1. High-pressure angle spur gears (35 deg pressure angle) running at high-speed provide improved
performance with similar bending and contact stress over more traditional gear pressure angles (20 deg). This was verified via analytical computer codes for efficiency, bending and contact stress analysis, as well as through experimental testing.
2. A general trend found from the experimental testing at identical conditions in the aerospace, jet-lubricated configuration was that the higher the pressure angle, the lower the temperature increase of the lubricant across the gearbox. This is an indication of the improved efficiency.
3. The space grease-lubricated tests conducted at 150 rpm and high load requires shrouding of the gear mesh to produce lower wear rates.
4. The high-pressure angle gears appeared to be better suited to the low-speed, high load, grease- lubricated conditions compared to the 3.18 and 2.12 module (8 and 12 pitch) gears with perfluoroether-based space grease.
References 1. Krantz, T., Oswald, F., and Handschuh, R., 2007, “Wear of Spur Gears Having a Dithering
Motion and Lubricated With a Perfluorinated Polyether Grease,” NASA/TM—2007-215008; ARL–TR–4124, December 2007.
2. Krantz, T., and Handschuh, R., 2005, “A Study of Spur Gears Lubricated With Grease-Observations From Seven Experiments,” NASA/TM— 2005-213957, ARL–TR–3159, September 2005.
3. Drago, R., Fundamentals of Gear Design (Butterworth, Stoneham, MA, 1988). 4. Dudley, D., Handbook of Practical Gear Design (McGraw-Hill, New York, NY, 1984). 5. Townsend, D., 1992, Dudley’s Gear Handbook, 2nd ed., McGraw-Hill, New York, NY. 6. Coy, J., Townsend, D., and Zaretsky, E., 1985, “Gearing,” Report No. NASA RP–1152.
NASA/TM—2010-216251/REV1 8
7. Hohn, B.-R., Michaelis, K., and Wimmer. A., 2006, “Gearboxes With Minimized Power Loss,” International Conference on Gears, September 2006, Munich Germany.
8. Schlecht, B., Martens, S., and Romhild, I., 2006, “Approaches to Oil-Free Gears,” International Conference on Gears, September 2006, Munich Germany.
9. Anderson, N., and Lowenthal, S., 1986, “Efficiency of Nonstandard and High Contact Ratio Involute Spur Gears,” ASME Journal of Mechanisms, Transmissions, and Automation in Design, 108, pp. 119–126.
10. ISO 6336 Gear Rating Program, Version 1.0, American Gear Manufacturers Association, 1997. 11. SolidWorks, CAD Venture Inc., Mentor, Ohio.
NASA/TM—2010-216251/REV1 9
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14. ABSTRACT A preliminary study has been completed to determine the feasibility of using high-pressure angle gears in aeronautic and space applications. Tests were conducted in the NASA GRC Spur Gear Test Facility at speeds up to 10,000 rpm and 73 N*m (648 in.-lb) for 3.18, 2.12, and 1.59 module gears (8, 12, and 16 diametral pitch gears), all designed to operate in the same test facility. The 3.18 module (8-diametral pitch), 28 tooth, 20 degree pressure angle gears are the NASA GRC baseline test specimen. Also, 2.12 module (12-diametral pitch), 42 tooth, 25 degree pressure angle gears were tested. Finally, 1.59 module (16-diametral pitch), 56 tooth, 35 degree pressure angle gears were tested. The high-pressure angle gears were the most efficient when operated in the high-speed aerospace mode (10,000 rpm, lubricated with a synthetic turbine engine oil) and produced the lowest wear rates when tested with a perfluoroether-based grease. The grease tests were conducted at 150 rpm and 71 N*m (630 in.-lb). 15. SUBJECT TERMS Gears; Transmissions
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